The Group of Seven (G7) has warned that it could escalate sanctions against Russia if the situation in eastern Ukraine spins further out of control.

G7 leaders said in a statement following talks in Brussels that it they "stand ready to intensify targeted sanctions and to consider significant additional restrictive measures to impose further costs on Russia should events so require."

“Russia’s illegal annexation of Crimea, and actions to destabilize eastern Ukraine are unacceptable and must stop," the leaders said in the statement. "These actions violate fundamental principles of international law and should be a concern for all nations."

The G7 also urged Russia to recognize the results of Ukraine's recent presidential election, complete the withdrawal of its troops on the border with Ukraine and stop the flow of weapons and militants.

German Chancellor Angela Merkel told reporters after the leaders’ working dinner on June 4 that the circumstances in eastern Ukraine cannot be allowed to deteriorate further and that Western leaders are ready to pressure Moscow into using its influence on pro-Russian separatists.

"If we do not have progress in the questions we have to solve, there is the possibility of sanctions -- even heavier Phase 3 sanctions -- on the table, because we cannot afford a further destabilization in Ukraine," Merkel said.

She added that Western governments would check "again and again" on the progress in Ukraine.

"The destabilization of the situation in eastern Ukraine has unfortunately continued very strongly in recent days," Merkel said.

French President Francois Hollande said the meeting sent a clear signal of unity by urging Russia to help stabilize the situation in Ukraine while keeping the threat of further sanctions on the table.

Russia had originally been slated to host the summit in its Black Sea resort of Sochi, but G7 leaders later moved the meeting to Brussels and disinvited Moscow as punishment for the Crimea annexation in March.

Russian President Vladimir Putin, however, is slated to meet with Merkel, Hollande, and British Prime Minister David Cameron this week on the sidelines of D-Day commemorations in France.

Ukrainian President-elect Petro Poroshenko is also set to attend the event, though no face-to-face meeting appeared to be scheduled with Putin as of June 5.

The G7 leaders welcomed Poroshenko’s election in the May 25 ballot in Ukraine, saying in the statement that they "commend him for reaching out to all the people of Ukraine."

"In the face of unacceptable interference in Ukraine’s sovereign affairs by the Russian Federation, we stand by the Ukrainian government and people," they said in the statement.

EU President Herman Van Rompuy said immediately prior to the June 4 talks that he would attend Poroshenko’s inauguration in Kyiv on June 7 in a show of solidarity for the embattled country’s new leadership.

Vice President Joseph Biden is expected to attend on behalf of the United States.